The 100(1 − α)% simultaneous confidence intervals for β obtained using
either Bonferroni Scheff 'e methods, provide confidence intervals for
each individual parameter β_j in such a way that the p'-dimensional region
formed by the intersection of the p'-simultaneous confidence intervals gives
at least a 100(1−α)% joint confidence region for all parameters. The shape
of this joint confidence region is rectangular or cubic. Scheff 'e also derives
an ellipsoidal 100(1 − α)% joint confidence region for all parameters that
is contained in the boxed region obtained by the Scheff 'e simultaneous confidence
intervals. This distinction is illustrated after joint confidence regions
are defined in the next section.